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Uniqueness of Solutions to the Stochastic Navier-Stokes, the Invariant Measure and Kolmogorov's Theory.

PDE and Applied Math Seminar

Speaker: Björn Birnir, University of California at Santa Barbara
Location: 3106 MSB
Start time: Wed, Feb 13 2008, 11:00AM

The existence and uniqueness of solutions of the Stochastic Navier-Stokes equation driven with additive noise in three dimensions is proven, in the presence of uni-directional mean flow and some swirl. The existence of a unique invariant measure is established and the properties of this measure are described. The invariant measure is used to prove Kolmogorov's scaling in 3-dimensional turbulence including the celebrated $-5/3$ power law for the decay of the power spectrum of a turbulent 3-dimensional flow.